For the TF relations to be successfully applied, the galaxies must have
detectable gas in essentially circular motion; otherwise,
the estimate of Vmax will be inaccurate.
Although there is occasionally detectable HI in lenticular
systems
(van Driel and van
Woerden 1991),
defining a
TF relation for E/S0 galaxies involves several complications:
the origin of the gas is uncertain,
the gas is usually patchy, its detection is difficult, and
its motion may not be circular. Because of these difficulties (and
the potential for significant M/L variations among early-type galaxies as
discussed in Sec. 7.3),
it is best to limit samples of galaxies to types Sb - Irr having no signs
of peculiar morphology, due, for example, to recent interactions. In addition,
the galaxies must have enough gas in their exterior regions such that
the observable rotation curve reaches a peak and Vmax can be
adequately sampled. It is now clear that disk galaxies within the
cores of even moderately poor clusters like Virgo suffer significant
stripping of their outer envelope of HI gas (e.g.,
Haynes and
Giovanelli 1986;
Cayatte et al. 1990).
Fortunately, only a few systems in Virgo
are gas-stripped to radii within the turn-over in their rotation curves.
The most serious cases also have morphological
peculiarities and would likely have been excluded on this basis alone
(e.g., NGC 4438). However, this remains an uncertainty for
galaxies in the cores of more distant clusters; for these galaxies a
full rotation curve may be necessary to assure that the rotation curves
do indeed turn over.

The modest morphological type dependence mentioned earlier (i.e.,
earlier types having low luminosities for their line-widths,
Sec. 7.2) is
a consequence of late-type galaxies being systematically bluer than
those of earlier type, coupled with the historical use of the B-band TF
relation.
Because the effect decreases dramatically toward longer wavelengths,
a likely cause is the smaller bulge-to-disk ratio and
the larger fraction of young stars in the low mass, gas-rich systems.
Some of the effect may also be the result of a decrease in
dust content for the later morphological types (e.g.,
van den Bergh and
Pierce 1990).
If so, the assumption
of a mean optical depth for all morphological types could contribute to
a morphological type dependence, especially at the shorter wavelengths
where extinction estimates would be significantly overestimated.

As mentioned above, the kinematics of lower luminosity irregular
galaxies become progressively more dominated by turbulence and less
by rotational motion. Consequently, the TF relations must progressively break
down below some luminosity.
Tully and
Fouqué (1985)
discuss the
line-width corrections for extending the TF relations to low luminosity
systems. Some of the motivation for this was to increase the number of
local calibrators available (e.g.,
Richter and
Huchtmeier 1984).
However,
the TF relations for systems fainter than MB ~ -15.0
become rather poorly defined
as the corrections to the line-widths become large and the inclinations become
more uncertain. With these factors in mind it is recommended that
samples be limited to galaxies brighter than MB ~
-16.0 for which the kinematics are dominated by rotation.